DataDrivenDMD.DMDPINV
— Typemutable struct DMDPINV <: DataDrivenDMD.AbstractKoopmanAlgorithm
Approximates the Koopman operator K
based on
K = Y / X
where Y
and X
are data matrices. Returns a Eigen
factorization of the operator.
Fields
Signatures
DataDrivenDMD.DMDSVD
— Typemutable struct DMDSVD{T} <: DataDrivenDMD.AbstractKoopmanAlgorithm
Approximates the Koopman operator K
based on the singular value decomposition of X
such that:
K = Y*V*Σ*U'
where Y
and X = U*Σ*V'
are data matrices. The singular value decomposition is truncated via the truncation
parameter, which can either be an Int
indiciating an index based truncation or a Real
indiciating a tolerance based truncation. Returns a Eigen
factorization of the operator.
Fields
truncation
Indiciates the truncation
Signatures
DataDrivenDMD.FBDMD
— Typemutable struct FBDMD{R} <: DataDrivenDMD.AbstractKoopmanAlgorithm
Approximates the Koopman operator K
via the forward-backward DMD. It is assumed that K = sqrt(K₁*inv(K₂))
, where K₁
is the approximation via forward and K₂
via DMDSVD. Based on this paper.
If truncation
∈ (0, 1) is given, the singular value decomposition is reduced to include only entries bigger than truncation*maximum(Σ)
. If truncation
is an integer, the reduced SVD up to truncation
is used for computation.
Fields
alg
Signatures
DataDrivenDMD.TOTALDMD
— Typemutable struct TOTALDMD{R, A} <: DataDrivenDMD.AbstractKoopmanAlgorithm
Approximates the Koopman operator K
with the algorithm alg
over the rank-reduced data matrices Xᵣ = X Qᵣ
and Yᵣ = Y Qᵣ
, where Qᵣ
originates from the singular value decomposition of the joint data Z = [X; Y]
. Based on this paper.
If rtol
∈ (0, 1) is given, the singular value decomposition is reduced to include only entries bigger than rtol*maximum(Σ)
. If rtol
is an integer, the reduced SVD up to rtol
is used for computation.
Fields
truncation
alg
Signatures